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44 //   sum_{i=0}^N polynomial(i) x^{N-i}.
48 // Evaluate the polynomial at x using the Horner scheme.
49 inline double EvaluatePolynomial(const Vector& polynomial, double x) {
51 for (int i = 0; i < polynomial.size(); ++i) {
52 v = v * x + polynomial(i);
58 // polynomial.
61 // Failure indicates that the polynomial is invalid (of size 0) or
66 bool FindPolynomialRoots(const Vector& polynomial,
70 // Return the derivative of the given polynomial. It is assumed that
71 // the input polynomial is at least of degree zero.
72 Vector DifferentiatePolynomial(const Vector& polynomial);
74 // Find the minimum value of the polynomial in the interval [x_min,
76 // derivative of the input polynomial. All real roots within the
80 void MinimizePolynomial(const Vector& polynomial,
108 // polynomial whose value and gradients are exactly equal to the ones
115 // Of course its possible to sample a polynomial any number of times,
120 // Interpolate the function described by samples with a polynomial,